The use of CO2 or gas as agents for a better recovery of oil in reservoirs has been used for many years. One difficulty is the occurrence of “fingering” resulting from viscous instability between the flooding fluid and the flooded fluid. Fingering is a complex non-linear mechanism difficult to estimate in real conditions and particularly when local reservoir heterogeneities that cannot be captured trigger the phenomenon.
The fundamental theory of fingering instability occurrence is well explained by the “Buckley-Leverett” model. See I. Brailovski et al. (“Fingering Instability in Water-Oil Displacement,” Transport in Porous Media (2006) Vol. 63. pp 363-380, hereinafter, “Brailovski”). The exact shape of fingering when occurring is very difficult to predict.
FIG. 1 is a series of 2D images 100 of fingering modeled in a Heleshaw tank, from De Wit, A., Bertho, Y. and Martin, M., “Viscous fingering of miscible slices,” Physics of Fluids, 17, 054114 (2005). In the series 100, a darker color fluid 110 is being pushed through a lighter color fluid 112, showing “Saffman-Taylor” instabilities and resulting in extended “fingers” such as finger 120, which can be of very long extension. The shapes of fingers are highly variable but as a rule they are shown to be “slender,” more or less 2 dimensional (contained in a high permeability layer) as can be seen in the modeled image of FIG. 1. FIG. 2 depicts results of numerical modeling of such instabilities from Brailovski. From the image 200, it can be seen that the instabilities can be of complicated shapes. The extension of the fingers is generally radial and each finger is rather slender.
Due to the difficulty in predicting the complex shapes of the flooding fronts of gas being injected into subterranean oil reservoirs, there is a need for techniques for monitoring such fronts.